The sum of an infinite geometric progression is `243` and the sum of its first five terms is `275` The first term of the progression

The sum of the terms of an infinite geometric progression is 3 and the sum of the squares of the terms is 81. Find the first term of the series.

The sum of an infinite geometric progression is 6, If the sum of the first two terms is 9//2 , then what is the first term?

The second term of an infinte geometric progression is 2 and its sum to infinity is 8. The first term is

The sum of an infinite geometric series is 6 and the sum of its first two terms is (9)/(2); find its common ratio.

The third term of a geometric progression is 4. Then find the product of the first five terms.

The first, second and seventh terms of an arithmetic progression (all the terms are distinct) are in geometric progression and the sum of these three terms is 93. Then, the fourth term of this geometric progression is

If the sum of the first 100 terms of an arithmetic progression is -1 and the sum of the even terms is 1, then the 100^("th") term of the arithmetic progression is

The sum of an infinite G.P. is 16 and the sum of the squares of its terms is 153(3)/(5) . Find the fourth term of the progression :